Anomalies, RG Flows, and the a-Theorem in 6d

The a-Theorem is a general constraint on unitary RG flows in even dimensions. I will describe the status of the a-Theorem in six dimensions, and prove it for a large class of supersymmetric flows. I will then explain how to compute the a-anomaly in six-dimensional SCFTs by relating it to the R-symmetry and gravitational anomalies of these theories. This leads to additional checks of the a-Theorem, and an interesting puzzle for theories with free gauge fields in the deep IR.